Putnam and Beyond 2nd Edition by Răzvan Gelca (PDF)

Description

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quadratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes’ theorem, analytical geometry, combinatorial geometry, and counting strategies.Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I first was introduced to the Putnam Exam several years ago in a class. At the time, I worked through some problems and found the book quite challenging. To tell the truth, I felt dumb. Years past, and I returned to it, and the book is much easier, but it is a great way to keep my math skills fresh, so much so that after purchasing the Kindle version, I bought the softcover and am working through the latter problems on paper. An excellent buy for the budding mathematician.

⭐I cant recommend this book to everyone. It is really only for a tiny percentage of students, even those who enjoy mathematics. Personally I feel like this book is catered towards the unchallenged first year undergrad, the problems sometimes require a high level of “comfortability” with abstraction and being able to wrestle with “difficult” problems.I feel as though there are books such as that of Larson’s which caters to a wider audience but the beautiful problems in this book just are not matched by any other problem solving book. Seriously though, very much recommended, it will help you grow in your mathematical ability as you fight with the problems, even if you don’t solve them.

⭐Upon first review, I see they have made some corrections from the first edition. Book came in good condition but the front cover seems to have been hastily cut near the bottom but it is negligible. Overall, I don’t mind since all of the pages are perfect. I would recommend this updated version from the 2007 version since some corrections have been made.

⭐+ problems with infinite radicals, continued fractions and infinite powers.- no heuristics- only 5 methods of proof.

⭐very good!

⭐Great book! The only thin is make sure you’ve taken up to Real Analysis if you really want to get the full understanding of the content but if you have then definately get this for the Putnam!

⭐goodgood

⭐My son loved

⭐It’s a book

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